Actually, we here have a theoretical separation of Church and State in the Constitution, but on a practical basis ....

When a previous recent Governor General went to church every Sunday, for the first time in Australia's history, it was no longer a private event, but because he (or perhaps it was his wife!) decreed it, became a State Event, and was advertised as such.

Parliament is opened with Prayer!

... and a lot of other 'incongruities', which at the time they were started, were not seen as such since CoE was effectively the 'State Religion' ... :-)